×

zbMATH — the first resource for mathematics

Deformation quantization and asymptotic operator representation. (English. Russian original) Zbl 0737.47042
Funct. Anal. Appl. 25, No. 3, 184-194 (1991); translation from Funkts. Anal. Prilozh. 25, No. 3, 24-36 (1991).
The asymptotic operator representation (AOR) based on the theory of pseudodifferential operators is studied in connection with the deformation quantization. The special local (AOR) defines the Čech 2- cocycle on certain variety. It is shown that if this cocycle gives a certain cohomology class, then the local (AOR) can be extended to the global one.
Reviewer: J.Kolomý (Praha)

MSC:
47G30 Pseudodifferential operators
47B99 Special classes of linear operators
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] M. V. Karasev and V. P. Maslov, ”Asymptotic and geometric quantization,” UMN,39, No. 6, 145-173 (1984).
[2] A. Lichnerowicz, Global Theory of Connections and Holonomy Groups [Russian translation], IL, Moscow (1960).
[3] B. V. Fedosov, ”Quantization and index,” Dokl. Akad. Nauk SSSR,291, No. 1, 82-86 (1986). · Zbl 0635.58019
[4] B. V. Fedosov, ”An index theorem in the algebra of quantum observables,” Dokl. Akad. Nauk SSSR,305, No. 4, 835-838 (1989).
[5] B. V. Fedosov, Index Theorems [in Russian] (in press). · Zbl 0884.58087
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.